I have Might and Magic VI: The Mandate of Heaven installed via Lutris (via the GOG installer) on Arch Linux. When I alt-tab out, then back in, the game keeps playing audio, but I don’t get the video back. It will either be a gray screen or a black screen. While troubleshooting, I also hit a situation where the game freezes in a similar way after skipping the opening cut-scene.
The happens regardless of Wine version and whether I’m using X11 or Wayland.
To fix this, in your Lutris library right click the game and go to Configure. Then in the Runner options tab, enable dgvoodoo2.
Additionally, if you find that some key bindings don’t work (e.g. Enter should put you into turn based mode), try another version of Wine/Proton. I had to use Proton 5.13 to get the all of the keys to work.